Tranny detent cable question

I seem to remember someone adjusting a "detent cable" on my dad's ETC when it was upshifting too early. (would sometimes start in 2nd and shift almost immediately to 3rd from a complete stop) After they tightened the cable, it shifted normally.

So the question is, would tightening that cable make the transmission downshift sooner? If so, how exactly is the cable tightened and which cable is it?